From 6c4cb0b91468ac0f7bc95d79f89b88417628127a Mon Sep 17 00:00:00 2001
From: letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7>
Date: Fri, 16 May 2008 12:21:36 +0000
Subject: Filename ZnZ (or Z_nZ in a later attempt) is neither pretty nor
 accurate (n _must_ in fact be a power of 2). Worse: Z_31Z is just plain wrong
 since it is Z/(2^31)Z and not Z/31Z (my fault).

As a consequence, switch to CyclicAxioms, Cyclic31, DoubleCyclic, etc



git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10940 85f007b7-540e-0410-9357-904b9bb8a0f7
---
 theories/Numbers/Cyclic/Int31/Cyclic31.v | 114 +++++++++++++++++++++++++++++++
 theories/Numbers/Cyclic/Int31/Z_31Z.v    | 114 -------------------------------
 2 files changed, 114 insertions(+), 114 deletions(-)
 create mode 100644 theories/Numbers/Cyclic/Int31/Cyclic31.v
 delete mode 100644 theories/Numbers/Cyclic/Int31/Z_31Z.v

(limited to 'theories/Numbers/Cyclic/Int31')

diff --git a/theories/Numbers/Cyclic/Int31/Cyclic31.v b/theories/Numbers/Cyclic/Int31/Cyclic31.v
new file mode 100644
index 000000000..49a1a0b5b
--- /dev/null
+++ b/theories/Numbers/Cyclic/Int31/Cyclic31.v
@@ -0,0 +1,114 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+(*i $Id$ i*)
+
+(** * Int31 numbers defines indeed a cyclic structure : Z/(2^31)Z *)
+
+(**
+Author: Arnaud Spiwack
+*)
+
+Require Export Int31.
+Require Import CyclicAxioms.
+
+Open Scope int31_scope.
+
+Definition int31_op : znz_op int31.
+ split.
+
+ (* Conversion functions with Z *)
+ exact (31%positive). (* number of digits *)
+ exact (31). (* number of digits *)
+ exact (phi). (* conversion to Z *)
+ exact (positive_to_int31). (* positive -> N*int31 :  p => N,i where p = N*2^31+phi i *)
+ exact head031.  (* number of head 0 *)
+ exact tail031.  (* number of tail 0 *)
+
+ (* Basic constructors *)
+ exact 0. (* 0 *)
+ exact 1. (* 1 *)
+ exact Tn. (* 2^31 - 1 *)
+ (* A function which given two int31 i and j, returns a double word
+    which is worth i*2^31+j *)
+ exact (fun i j => match (match i ?= 0 with | Eq =>  j ?= 0 | not0 => not0 end) with | Eq => W0 | _ => WW i j end).
+ (* two special cases where i and j are respectively taken equal to 0 *)
+ exact (fun i => match i ?= 0 with | Eq => W0 | _ => WW i 0 end).
+ exact (fun j => match j ?= 0 with | Eq => W0 | _ => WW 0 j end).
+
+ (* Comparison *)
+ exact compare31.
+ exact (fun i => match i ?= 0 with | Eq => true | _ => false end).
+
+ (* Basic arithmetic operations *)
+ (* opposite functions *)
+ exact (fun i => 0 -c i).
+ exact (fun i => 0 - i).
+ exact (fun i => 0-i-1). (* the carry is always -1*)
+ (* successor and addition functions *)
+ exact (fun i => i +c 1).
+ exact add31c.
+ exact add31carryc.
+ exact (fun i => i + 1).
+ exact add31.
+ exact (fun i j => i + j + 1).
+ (* predecessor and subtraction functions *)
+ exact (fun i => i -c 1).
+ exact sub31c.
+ exact sub31carryc.
+ exact (fun i => i - 1).
+ exact sub31.
+ exact (fun i j => i - j - 1).
+ (* multiplication functions *)
+ exact mul31c.
+ exact mul31.
+ exact (fun x => x *c x).
+
+ (* special (euclidian) division operations *)
+ exact div3121.
+ exact div31. (* this is supposed to be the special case of division a/b where a > b *)
+ exact div31.
+ (* euclidian division remainder *)
+ (* again special case for a > b *)
+ exact (fun i j => let (_,r) := i/j in r).
+ exact (fun i j => let (_,r) := i/j in r).
+ (* gcd functions *)
+ exact gcd31. (*gcd_gt*)
+ exact gcd31. (*gcd*)
+ 
+ (* shift operations *)
+ exact addmuldiv31. (*add_mul_div  *)
+(*modulo 2^p  *)
+ exact (fun p i => 
+     match compare31 p 32 with
+     | Lt => addmuldiv31 p 0 (addmuldiv31 (31-p) i 0)
+     | _ => i
+     end).
+
+ (* is i even ? *)
+ exact (fun i => let (_,r) := i/2 in 
+                          match r ?= 0 with
+                          | Eq => true
+                          | _ => false
+                          end).
+
+ (* square root operations *)
+ exact sqrt312. (* sqrt2 *)
+ exact sqrt31. (* sqr *)
+Defined.
+
+
+Definition int31_spec : znz_spec int31_op.
+Admitted.
+
+
+Module Int31Cyclic <: CyclicType.
+  Definition w := int31.
+  Definition w_op := int31_op.
+  Definition w_spec := int31_spec.
+End Int31Cyclic.
diff --git a/theories/Numbers/Cyclic/Int31/Z_31Z.v b/theories/Numbers/Cyclic/Int31/Z_31Z.v
deleted file mode 100644
index 3b5944ed3..000000000
--- a/theories/Numbers/Cyclic/Int31/Z_31Z.v
+++ /dev/null
@@ -1,114 +0,0 @@
-(************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
-(*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
-(************************************************************************)
-
-(*i $Id$ i*)
-
-(** * Int31 numbers defines indeed a cyclic structure : Z/31Z *)
-
-(**
-Author: Arnaud Spiwack
-*)
-
-Require Export Int31.
-Require Import Z_nZ.
-
-Open Scope int31_scope.
-
-Definition int31_op : znz_op int31.
- split.
-
- (* Conversion functions with Z *)
- exact (31%positive). (* number of digits *)
- exact (31). (* number of digits *)
- exact (phi). (* conversion to Z *)
- exact (positive_to_int31). (* positive -> N*int31 :  p => N,i where p = N*2^31+phi i *)
- exact head031.  (* number of head 0 *)
- exact tail031.  (* number of tail 0 *)
-
- (* Basic constructors *)
- exact 0. (* 0 *)
- exact 1. (* 1 *)
- exact Tn. (* 2^31 - 1 *)
- (* A function which given two int31 i and j, returns a double word
-    which is worth i*2^31+j *)
- exact (fun i j => match (match i ?= 0 with | Eq =>  j ?= 0 | not0 => not0 end) with | Eq => W0 | _ => WW i j end).
- (* two special cases where i and j are respectively taken equal to 0 *)
- exact (fun i => match i ?= 0 with | Eq => W0 | _ => WW i 0 end).
- exact (fun j => match j ?= 0 with | Eq => W0 | _ => WW 0 j end).
-
- (* Comparison *)
- exact compare31.
- exact (fun i => match i ?= 0 with | Eq => true | _ => false end).
-
- (* Basic arithmetic operations *)
- (* opposite functions *)
- exact (fun i => 0 -c i).
- exact (fun i => 0 - i).
- exact (fun i => 0-i-1). (* the carry is always -1*)
- (* successor and addition functions *)
- exact (fun i => i +c 1).
- exact add31c.
- exact add31carryc.
- exact (fun i => i + 1).
- exact add31.
- exact (fun i j => i + j + 1).
- (* predecessor and subtraction functions *)
- exact (fun i => i -c 1).
- exact sub31c.
- exact sub31carryc.
- exact (fun i => i - 1).
- exact sub31.
- exact (fun i j => i - j - 1).
- (* multiplication functions *)
- exact mul31c.
- exact mul31.
- exact (fun x => x *c x).
-
- (* special (euclidian) division operations *)
- exact div3121.
- exact div31. (* this is supposed to be the special case of division a/b where a > b *)
- exact div31.
- (* euclidian division remainder *)
- (* again special case for a > b *)
- exact (fun i j => let (_,r) := i/j in r).
- exact (fun i j => let (_,r) := i/j in r).
- (* gcd functions *)
- exact gcd31. (*gcd_gt*)
- exact gcd31. (*gcd*)
- 
- (* shift operations *)
- exact addmuldiv31. (*add_mul_div  *)
-(*modulo 2^p  *)
- exact (fun p i => 
-     match compare31 p 32 with
-     | Lt => addmuldiv31 p 0 (addmuldiv31 (31-p) i 0)
-     | _ => i
-     end).
-
- (* is i even ? *)
- exact (fun i => let (_,r) := i/2 in 
-                          match r ?= 0 with
-                          | Eq => true
-                          | _ => false
-                          end).
-
- (* square root operations *)
- exact sqrt312. (* sqrt2 *)
- exact sqrt31. (* sqr *)
-Defined.
-
-
-Definition int31_spec : znz_spec int31_op.
-Admitted.
-
-
-Module Int31_words <: CyclicType.
-  Definition w := int31.
-  Definition w_op := int31_op.
-  Definition w_spec := int31_spec.
-End Int31_words.
-- 
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